Current MRI, CT, and PET image reconstruction algorithms are limited by the large interpolation errors of the nonuniform data in the Fourier space. This is becoming a computational bottleneck in large-scale 3D imaging where the size of data grows rapidly with the size of volume and the increasing demand on high resolution. The proposed research would develop multidimensional nonuniform fast Fourier transform (NUFFT) algorithms. Such algorithms will significantly improve both the resolution and the speed of image reconstruction because of the highly accurate and efficient interpolation. The NUFFT will be applied to and evaluated by magnetic resonance imaging (MRI), positron emission tomography (PET), and X-ray computerized tomography (CT). A joint inversion framework will also be developed for the MRI/PET combination and for the CT/PET combination to improve the information obtained by individual modalities. In the R21 Phase I of this research, we will (a) develop new 2D nonuniform fast Fourier transform (NUFFT) algorithms; (b) evaluate the NUFFT algorithms with synthetic and real MRI and CT data from the Duke Center for In Vivo Microscopy. In the R33 Phase II of this research, we will (a) develop 3D NUFFT algorithms for MRT, CT and PET imaging modalities, (b) develop a joint inversion framework based on NUFFT for multi-modality imaging in the MRI/PET and CT/PET combinations, and (c) evaluate the 3D NUFFT and joint inversion framework with synthetic and real MRI/PET and CT/PET data. Such a framework can be considered as a shift in computational paradigm for image reconstruction in MRI, PET, CT, and potentially many other modalities. For rapidly growing 3D imaging applications, the new NUFFT algorithms would improve the resolution and computation speed over the conventional methods by orders of magnitude. The joint inversion method will improve the information obtained by the individual modalities.